Covariant Formulation Research Articles

Targeted optimal treatment regime learning using summary statistics

Summary Personalized decision-making, aiming to derive optimal treatment regimes based on individual characteristics, has recently attracted increasing attention in many fields, such as medicine, social services and economics. Current literature mainly focuses on estimating treatment regimes from a single source population. In real-world applications, the distribution of a target population can be different from that of the source population. Therefore, treatment regimes learned by existing methods may not generalize well to the target popu- lation. Because of privacy concerns and other practical issues, individual-level data from the target population are often not available, which makes treatment regime learning more challenging. We consider the problem of treatment regime estimation when the source and target populations may be heterogeneous, individual-level data are available from the source population and only the summary information of covariates, such as moments, is accessible from the target population. We develop a weighting framework that tailors a treatment regime for a given target population by leveraging the available summary statistics. Specifically, we propose a calibrated augmented inverse probability weighted estimator of the value function for the target population and estimate an optimal treatment regime by maximizing this estimator within a class of prespecified regimes. We show that the proposed calibrated estimator is consistent and asymptotically normal even with flexible semi/nonparametric models for nuisance function approximation, and that the variance of the value estimator can be consistently estimated. We demonstrate the empirical performance of the proposed method using simulation studies and a real application using two datasets on sepsis.

How Much Perioperative Pain and Dysfunction Underlie the HOOS JR and KOOS JR?

The Hip Disability and Osteoarthritis Outcome Score Joint Replacement (HOOS JR) and Knee Injury and Osteoarthritis Outcome Score Joint Replacement (KOOS JR) scores represent pain and dysfunction as a single number ranging from 0 (extreme pain and dysfunction) to 100 (no pain or functional limitations). However, scores between 0 and 100 lack a simple interpretation because they reflect varying combinations of pain levels and dysfunction. Given that most adverse events and improvement occur within the first 90 days after surgery, a deeper understanding of the level of pain and dysfunction may reveal missed opportunities for patient care. (1) What does a given preoperative or postoperative HOOS JR and KOOS JR score indicate about pain and ability to perform daily activities? (2) How much of a change in score (that is, delta) is needed to indicate significant improvement in pain control and daily functioning? The Michigan Arthroplasty Registry Collaborative Quality Initiative contains more than 95% of THAs and TKAs performed in Michigan. Between January 2017 and March 2019, 84,175 people in the registry underwent primary THA or TKA and were potentially eligible for this retrospective, comparative study of the first 90 postoperative days. Eighty-four percent (70,608 of 84,175) were excluded because their surgeons did not attain a target survey collection proportion of 70% and another 6% (5042) were missing covariate information or surveys, leaving 10% (8525) for analysis. The mean age and percentage of women were 65 ± 11 years and 55% (2060 of 3716), respectively, for patients undergoing THA and 67 ± 9 years and 61% (2936 of 4809), respectively, for those undergoing TKA. There were no clinically meaningful differences between patients who were analyzed and those who were excluded except for lower representation of non-White patients in the analyzed group. For interpretation, patient responses to Question 7 (pain) and Question 6 (function) from the Patient-Reported Outcomes Measurement Information System global items (PROMIS-10) were dichotomized into "much pain" (rating of pain 4 to 10 of 10) versus "less pain" (rating of ≤ 3) and "good function" (able to perform most activities) versus "poor function" (not able to perform most activities) and combined into four pain-function categories. We examined the mean preoperative and postoperative HOOS JR and KOOS JR scores for each pain-function category, adjusted for patient characteristics. We calculated the size of the delta associated with an increase to a more favorable category postoperatively (versus staying in the same or worse category) via multivariable logistic regression that controlled for patient characteristics. Patients in the least favorable "much pain, poor function" category preoperatively had adjusted mean scores of 40 (95% confidence interval 39 to 41) for both the HOOS JR and KOOS JR. Those with mixed levels of pain and function had mean scores between 46 and 55. Those in the most favorable "less pain, good function" category had means of 60 (95% CI 58 to 62) and 59 (95% CI 58 to 61) for the HOOS JR and KOOS JR, respectively. The adjusted delta to achieve a pain level of ≤ 3 or the ability to perform most activities was 30 (95% CI 26 to 36) on the HOOS JR and 27 (95% CI 22 to 29) on the KOOS JR scales. These adjusted means of the HOOS JR and KOOS JR provide context for understanding the levels of pain and dysfunction for individuals as well for patients reported in other studies. Potential quality improvement efforts could include tracking the proportion of patients with THA or TKA who achieved a sufficient delta to attain pain levels of ≤ 3 or the ability to perform most activities. Future studies are needed to understand pain and function represented by the HOOS JR and KOOS JR at 1 to 2 years, how these may differ by patient subgroups, and whether scores can be improved through quality improvement efforts. Level III, therapeutic study.

Einstein and Jordan-frame covariant Hamiltonians for F(R) gravity and their canonical relationships

This paper is devoted to the analysis of the covariant canonical formalism of F(R) gravity in Einstein frame. We also find canonical transformation between covariant canonical formulation of F(R) gravity in Jordan frame and Einstein frames and we also determine corresponding generating function.

A synthetic data integration framework to leverage external summary-level information from heterogeneous populations.

There is a growing need for flexible general frameworks that integrate individual-level data with external summary information for improved statistical inference. External information relevant for a risk prediction model may come in multiple forms, through regression coefficient estimates or predicted values of the outcome variable. Different external models may use different sets of predictors and the algorithm they used to predict the outcome Y given these predictors may or may not be known. The underlying populations corresponding to each external model may be different from each other and from the internal study population. Motivated by a prostate cancer risk prediction problem where novel biomarkers are measured only in the internal study, this paper proposes an imputation-based methodology, where the goal is to fit a target regression model with all available predictors in the internal study while utilizing summary information from external models that may have used only a subset of the predictors. The method allows for heterogeneity of covariate effects across the external populations. The proposed approach generates synthetic outcome data in each external population, uses stacked multiple imputation to create a long dataset with complete covariate information. The final analysis of the stacked imputed data is conducted by weighted regression. This flexible and unified approach can improve statistical efficiency of the estimated coefficients in the internal study, improve predictions by utilizing even partial information available from models that use a subset of the full set of covariates used in the internal study, and provide statistical inference for the external population with potentially different covariate effects from the internalpopulation.

Broad Minimax Probability Learning System and its Application in Regression Modeling

Broad learning system (BLS), a novel incremental learning algorithm, has attracted more and more attention and application. BLS achieves a perfect balance between learning performance and modeling efficiency based on the mean square error (MSE) criterion. However, MSE assumes that a random error between an observed value and real value is a Gaussian distribution, which may be inconsistent to the real-world situation. Moreover, the distributional assumptions may cast doubt on the generalization and validity of the built BLS model. In this article, we propose a novel distribution-free BLS for regression analysis, called broad minimax probability learning system (BMPLS). Learning from the idea of minimax probability machine regression, BMPLS builds a regression model by maximizing the worst probability of the regression function being within the allowed error range. It adequately utilizes the mean and covariance information of the hidden-space feature without making any distributional assumptions of the random error. In order to further improve the learning performance of the model, a regularized BMPLS (RBMPLS) is proposed by applying elastic-net regularization term to BMPLS. The corresponding optimization algorithm is also designed for calculating the output weights of the model. Multiple experiments based on public datasets were carried out to demonstrate the feasibility of the proposed algorithms.

Abstract 02: Intergenerational Socioeconomic Mobility is Associated With Adulthood All-Cause Mortality in the Hispanic Community Health Study/Study of Latinos

Introduction: Different patterns of socioeconomic mobility (SEM) across the life course may influence the risk of all-cause mortality in adulthood. Lifetime low socioeconomic status and downward social mobility may be associated with a higher risk of mortality. Hypothesis: SEM is associated with mortality, and persons with enduring intergenerational adversity or downward SEM have a higher risk of mortality compared to persons with enduring intergenerational advantage. Methods: This study included 13,459 participants, 18-74 years of age, from the Hispanic Community Health Study/Study of Latinos who participated in the baseline visit (2008-2011) and were not missing key covariate information. Socioeconomic position (SEP) was assessed as parental education in childhood (dichotomized at high school), and a 5-facet index of SEP in adulthood across education, income, employment status, longest held occupation type, and homeownership. The adulthood SEP index was dichotomized at the median value of 2 (range: 0-5). Childhood and adulthood SEP were then combined into a single 4-level measure of SEM (enduring advantage, upward mobility, downward mobility, and enduring adversity). Multivariable sampling weight-adjusted Cox proportional hazards regression was performed to estimate the association between SEM and all-cause mortality. Potential confounders included age, gender, Hispanic/Latino ethnic background, US nativity, years spent in the US, and study center, whereas alcohol and tobacco use, depression score, and BMI were considered potential mediators. Presence of mediation was assessed by calculating total and direct effects via modeling, then evaluating percent change from total to direct effects against a 10% guideline. Results: During the follow-up period of 2008-2019, 515 deaths were recorded. After adjusting for all potential confounders, a significant association was found between adulthood all-cause mortality and SEM overall (F = 7.62, p < 0.0001). Downward mobility had significantly higher hazard of death compared to enduring advantage (aHR: 1.81, 95% CI: 1.17-2.81), although upward mobility and enduring adversity groups were not significant. The direct effect for downward mobility was reduced after adjustment for potential mediators (aHR: 1.49, 95% CI: 0.96, 2.30). Conclusions: Socioeconomic mobility, specifically downward mobility, is associated with all-cause mortality among a diverse cohort of Hispanic/Latino individuals residing in the United States. This association shows evidence of mediation by clinical and behavioral characteristics.

Hamilton’s equations in the covariant teleparallel equivalent of general relativity

We present Hamilton's equations for the teleparallel equivalent of general relativity (TEGR), which is a reformulation of general relativity based on a curvatureless, metric compatible, and torsionful connection. For this, we consider the Hamiltonian for TEGR obtained through the vector, antisymmetric, symmetric and trace-free, and trace irreducible decomposition of the phase space variables. We present the Hamiltonian for TEGR in the covariant formalism for the first time in the literature, by considering a spin connection depending on Lorentz matrices. We introduce the mathematical formalism necessary to compute Hamilton's equations in both Weitzenbock gauge and covariant formulation, where for the latter we must introduce new fields: Lorentz matrices and their associated momenta. We also derive explicit relations between the conjugate momenta of the tetrad and the conjugate momenta for the metric that are traditionally defined in GR, which are important to compare both formalisms.

Conjugate Modeling Approaches for Small Area Estimation with Heteroscedastic Structure

AbstractSmall area estimation (SAE) has become an important tool in official statistics, used to construct estimates of population quantities for domains with small sample sizes. Typical area-level models function as a type of heteroscedastic regression, where the variance for each domain is assumed to be known and plugged in following a design-based estimate. Recent work has considered hierarchical models for the variance, where the design-based estimates are used as an additional data point to model the latent true variance in each domain. These hierarchical models may incorporate covariate information but can be difficult to sample from in high-dimensional settings. Utilizing recent distribution theory, we explore a class of Bayesian hierarchical models for SAE that smooth both the design-based estimate of the mean and the variance. In addition, we develop a class of unit-level models for heteroscedastic Gaussian response data. Importantly, we incorporate both covariate information as well as spatial dependence, while retaining a conjugate model structure that allows for efficient sampling. We illustrate our methodology through an empirical simulation study as well as an application using data from the American Community Survey.

A cumulative exposure model for remaining useful life prediction of pitot tube based on dynamic operating data

AbstractThe data measured by the pitot tube (PT) is related to airspeed indication and flight safety. However, there are few methods to solve the problem of failure prediction and predictive maintenance of PT. This study proposes a method for predicting the remaining useful life (RUL) of the PT based on dynamic operating data. First, an exposure index (EI) characterizing the severity level of operating conditions is proposed based on multiple dynamic operating and environmental parameters, then a cumulative exposure model (CEM) is developed to calculate the cumulative exposure. Dynamic covariate information is incorporated into the time‐to‐failure distribution of PT through the CEM, the RUL distribution of the individual PT is then obtained by Monte Carlo simulation. A case study is carried out based on actual data of a commercial aircraft fleet and shows that the proposed CEM can effectively use historical aircraft environmental information and truncated failure data of the components. The relative error of the remaining life prediction is substantially improved compared to the traditional reliability analysis methods, which means that the proposed model can provide more reliable RUL results based on historical operating conditions, providing better support for PT risk assessment and condition‐based maintenance decisions.

Incorporating Covariates into Measures of Surrogate Paradox Risk.

Clinical trials often collect intermediate or surrogate endpoints other than their true endpoint of interest. It is important that the treatment effect on the surrogate endpoint accurately predicts the treatment effect on the true endpoint. There are settings in which the proposed surrogate endpoint is positively correlated with the true endpoint, but the treatment has opposite effects on the surrogate and true endpoints, a phenomenon labeled "surrogate paradox". Covariate information may be useful in predicting an individual's risk of surrogate paradox. In this work, we propose methods for incorporating covariates into measures of assessing the risk of surrogate paradox using the meta-analytic causal association framework. The measures calculate the probability that a treatment will have opposite effects on the surrogate and true endpoints and determine the size of a positive treatment effect on the surrogate endpoint that would reduce the risk of a negative treatment effect on the true endpoint as a function of covariates, allowing the effects of covariates on the surrogate and true endpoint to vary across trials.

Trace anomaly and induced action for a metric-scalar background

The conformal anomaly and anomaly-induced effective action represent useful and economic ways to describe semiclassical contributions to the action of gravity. We discuss the anomaly in the case when the background is formed by metric and scalar fields and formulate the induced action in two standard covariant forms. The analysis of induced action at low energies reveals existing connection to the renormalization group and effective potential. The classification of anomalous terms is extended to the scalar background and ambiguities in the total derivative terms in the anomaly are considered using Pauli–Villars regularization.

Two‐stage distributionally robust optimization model for a pharmaceutical cold supply chain network design problem

AbstractPharmaceutical safety has received increasing attention from governments and corporations, and building a safe and effective pharmaceutical cold supply chain network has become an important issue. This paper proposes a two‐stage pharmaceutical cold supply chain network design problem considering drug safety, in which the drug demand, transportation costs, and drug safety risk costs are assumed to be random variables. Due to the presence of uncertainty and the fact that information about the distribution of uncertain parameters is often only partially known, a distributionally robust optimization method is used to handle the uncertainty. A two‐stage distributionally robust optimization model is constructed, in which the reliability of the estimation of the demand necessary to satisfy the entire cold chain network is ensured to be greater than a certain predetermined level by introducing an ambiguous joint chance constraint. The decision process for the problem can be divided into strategic and operational decisions with the goal of minimizing the total costs related to facility construction, the purchase of raw materials, drug production, transportation, and safety risks. By introducing an ambiguity set with mean and covariance information to describe the uncertain parameters, the two‐stage model is eventually reformulated as a standard second‐order cone program, thus making it computationally tractable. Finally, numerical experiments are presented to demonstrate the effectiveness of the proposed models and optimization methods.

COVID-19 transmission risk in Surabaya and Sidoarjo: an inhomogeneous marked Poisson point process approach.

Understanding the spatio-temporal dynamics of COVID-19 transmission is necessary to plan better strategies for controlling the spread of the disease. However, only a few studies explore the COVID-19 transmission risk over a fine spatial resolution while considering relevant spatial and temporal factors. To this aim, we consider an inhomogeneous marked Poisson point process model to assess COVID-19 transmission risk using data of home addresses of confirmed cases, in relation to locations of sources of crowd (enterprise, market, and place of worship) and population density in Surabaya and Sidoarjo, Indonesia. Our marked model is able to analyze how the spatial covariates are varying with time, helping authorities to evaluate the information of covariates depending on the period in which restrictions are taking place. Our results show that enterprise, place of worship, and population densities have significant impact to the transmission risk in Surabaya and Sidoarjo. We finally provide predicted risk maps which provide additional information based on the demographic-based risk analysis to help conduct more efficient testing, tracing, and vaccination programs.

A 3+1 formulation of the 1/c expansion of General Relativity

Expanding General Relativity in the inverse speed of light, 1/c, leads to a nonrelativistic gravitational theory that extends the Post-Newtonian expansion by the inclusion of additional strong gravitational potentials. This theory has a fully covariant formulation in the language of Newton-Cartan geometry but we revisit it here in a 3+1 formulation. The appropriate 3+1 formulation of General Relativity is one first described by Kol and Smolkin (KS), rather than the better known Arnowitt-Deser-Misner (ADM) formalism. As we review, the KS formulation is dual to the ADM formulation in that the role of tangent and co-tangent spaces get interchanged. In this 3+1 formulation the 1/c expansion can be performed in a more systematic and efficient fashion, something we use to extend the computation of the effective Lagrangian beyond what was previously achieved and to make a number of new all order observations.

Model misspecification and robust analysis foroutcome-dependent sampling designs under generalizedlinear models.

Outcome-dependent sampling (ODS) is a commonly used class of sampling designs to increase estimation efficiency in settings where response information (and possibly adjuster covariates) is available, but the exposure is expensive and/or cumbersome to collect. We focus on ODS within the context of a two-phase study, where in Phase One the response and adjuster covariate information is collected on a large cohort that is representative of the target population, but the expensive exposure variable is not yet measured. In Phase Two, using response information from Phase One, we selectively oversample a subset of informative subjects in whom we collect expensive exposure information. Importantly, the Phase Two sample is no longer representative, and we must use ascertainment-correcting analysis procedures for valid inferences. In this paper, we focus on likelihood-based analysis procedures, particularly a conditional-likelihood approach and a full-likelihood approach. Whereas the full-likelihood retains incomplete Phase One data for subjects not selected into Phase Two, the conditional-likelihood explicitly conditions on Phase Two sample selection (ie,it is a "complete case" analysis procedure). These designs and analysis procedures are typically implemented assuming a known, parametric model for the response distribution. However, in this paper, we approach analyses implementing a novel semi-parametric extension to generalized linear models (SPGLM) to develop likelihood-based procedures with improved robustness to misspecification of distributional assumptions. We specifically focus on the common setting where standard GLM distributional assumptions are not satisfied (eg,misspecified mean/variance relationship). We aim to provide practical design guidance and flexible tools for practitioners in these settings.

Covariate Dependent Sparse Functional Data Analysis

This study proposes a method to incorporate covariate information into sparse functional data analysis. The method aims at cases where each subject has a limited number of longitudinal measurements and is associated with static covariates. This research is motivated by several use cases in practice. One representative example is void swelling, a nuclear-specific material degradation mechanism. Void swelling is affected by many covariates, including alloy composition and irradiation type. How to accurately model the complicated joint effects of such covariates on the swelling process is the key to mitigating the effect of swelling and ensuring safe operation. Unlike most of the existing methods, the proposed method can handle high-dimensional covariates with the informative covariate identification procedure and sparse and irregularly spaced measurements, that is, does not require complete or dense observations. The main innovation of the proposed method is that we model the variation coming from covariates and the variation left conditioned on covariates, such that the functional principal component analysis and Gaussian process can be conducted in a unified manner. We also propose a systematic approach to identify important covariates in the hypothesis testing context. The methodology is demonstrated on applications in nuclear engineering and healthcare and simulation studies.History: Bianca Maria Colosimo served as senior editor for this article.Funding: This work was supported in part by the Air Force Office of Scientific Research [Grant FA9550-20-1-0072] and in part by the Department of Energy [Award DE-NE0008993].Data Ethics & Reproducibility Note: No data ethics considerations are foreseen related to this article. The code capsule is available on Code Ocean at https://codeocean.com/capsule/9363709 and in the e-Companion to this article (available at https://doi.org/10.1287/ijds.2023.0025 ).

Application of Recurrent Neural-Network based Kalman Filter for Uncertain Target Models

For various target tracking applications, it is well known that the Kalman filter is the optimal estimator(in the minimum mean-square sense) to predict and estimate the state(position and/or velocity) of linear dynamical systems driven by Gaussian stochastic noise. In the case of nonlinear systems, Extended Kalman filter(EKF) and/or Unscented Kalman filter(UKF) are widely used, which can be viewed as approximations of the(linear) Kalman filter in the sense of the conditional expectation. However, to implement EKF and UKF, the exact dynamical model information and the statistical information of noise are still required. In this paper, we propose the recurrent neural-network based Kalman filter, where its Kalman gain is obtained via the proposed GRU-LSTM based neural-network framework that does not need the precise model information as well as the noise covariance information. By the proposed neural-network based Kalman filter, the state estimation performance is enhanced in terms of the tracking error, which is verified through various linear and nonlinear tracking problems with incomplete model and statistical covariance information.

An Analytic Benchmark for Neutron Boltzmann Transport with Downscattering: Part III. Uncertainty Propagation and Multigroup Covariance Matrices

An analytic benchmark for nuclear data uncertainty propagation in k-eigenvalue calculations is demonstrated. Flat-flux-weighted cross-section covariance matrices are available in the ENDF/B library for many isotopes. For application-specific purposes, flux-weighted multigroup cross sections with carefully constructed energy group boundaries are desired. In this paper, we use the covariance information from ENDF/B-VII.1 for the defined continuous-energy cross section and an artificially inflated variance version of the same covariance matrix for first-order and Monte Carlo propagation of uncertainty calculations. A flat-flux weighting function is used for the continuous-energy cross-section uncertainty collapse resulting in a higher propagated uncertainty on the k-eigenvalue as the group structure becomes coarser. The results of this analytic benchmark suggest that the reporting of flat-flux-weighted multigroup cross-section covariance matrices at the ENDF level may lead to inaccurate predictions of the uncertainty on the k-eigenvalue for certain applications. This work implies that not only should the resonance parameter uncertainties that go into the calculation of the continuous-energy cross sections be published, but the parameter uncertainties should also be processed into continuous-energy cross-section uncertainties that can be collapsed to application-specific multigroup cross-section covariance matrices.

Constant primary operators and where to find them: the strange case of BPS defects in ABJ(M) theory

We investigate the one-dimensional defect SCFT defined on the 1/2 BPS Wilson line/loop in ABJ(M) theory. We show that the supermatrix structure of the defect imposes a covariant supermatrix representation of the supercharges. Exploiting this covariant formulation, we prove the existence of a long multiplet whose highest weight state is a constant supermatrix operator. At weak coupling, we study this operator in perturbation theory and confirm that it acquires a non-trivial anomalous dimension. At strong coupling, we conjecture that this operator is dual to the lowest bound state of fluctuations of the fundamental open string in AdS4 × ℂℙ3 around the classical 1/2 BPS solution. Quite unexpectedly, this operator also arises in the cohomological equivalence between bosonic and fermionic Wilson loops. We also discuss some regularization subtleties arising in perturbative calculations on the infinite Wilson line.

New product life cycle curve modeling and forecasting with product attributes and promotion: A Bayesian functional approach

New products are highly valued by manufacturers and retailers due to their vital role in revenue generation. Product life cycle (PLC) curves often vary by their shapes and are complicated by promotional activities that induce spiky and irregular behaviors. We collaborate with JD.com to develop a flexible PLC curve forecasting framework based on Bayesian functional regression that accounts for useful covariate information, including product attributes and promotion. The functional model treats PLC curves as target variables and includes both scalar and functional predictors, capturing time‐varying promotional activities. Harnessing the power of basis function transformation, the developed model can effectively characterize the local features and temporal evolution of sales curves. Our Bayesian framework can generate initial curve forecasts before the product launch and update the forecasts dynamically as new sales data are collected. We validate the superior performance of our method through extensive numerical experiments using three real‐world data sets. Our forecasting framework reduces the forecasting error by 5.35%–30.76% over JD.com's current model and outperforms alternative models significantly. Furthermore, the estimated promotion effect function provides useful insights into how promotional activities interact with sales curves.